Problem: Amira has $\dfrac34$ of a bag of cat food. Her cat eats $\dfrac{1}{10}$ of a bag per week. How many weeks will the food last?
We can think about this problem like this: $ {\text{number of weeks}} = \dfrac{{\text{all the cat food}}} {{\text{amount eaten per week}}}$ ${\text{?}} = {\dfrac34} \text{ bag} \div {\dfrac{1}{10}} \text{ bag}$ $\begin{aligned} {\dfrac34} \div {\dfrac{1}{10}}&={\dfrac34}\times\dfrac{10}{1} \\\\ &=\dfrac{3\times10}{4\times1} \\\\ &=\dfrac{30}{4} \\\\ &=\dfrac{15}{2} \end{aligned}$ The bag of cat food will last for $\dfrac{15}{2}$ weeks.